Reduced Compton Wavelength of Electron

Theorem

The Compton wavelength of the electron is:

\(\ds \lambdabar_\E\)

\(\approx\)

\(\ds 3 \cdotp 86159 \, 267 \times 10^{-13} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 3 \cdotp 86159 \, 267 \times 10^{-11} \, \mathrm {cm}\)

Symbol

$\lambdabar_\E$

The symbol for the reduced Compton wavelength of the electron is $\lambdabar_\E$.

The $\LaTeX$ code for \(\lambdabar_\E\) is \lambdabar_\E .

Proof

By definition, the reduced Compton wavelength $\lambdabar_\E$ of an electron is given as:

$\lambdabar_\E = \dfrac {\lambda_\E} {2 \pi}$

where $\lambda_\E$ denotes the Compton wavelength of the electron.

Then we have:

\(\ds \lambda_\E\)

\(\approx\)

\(\ds 2 \cdotp 42631 \, 02386 \, 7(73) \times 10^{-12} \, \mathrm m\)

Compton Wavelength of Electron

\(\ds \leadsto \ \ \)

\(\ds \lambdabar_\E\)

\(\approx\)

\(\ds \dfrac {2 \cdotp 42631 \, 02386 \, 7(73) \times 10^{-12} } {2 \pi} \, \mathrm m\)

\(\ds \)

\(\approx\)

\(\ds 3 \cdotp 86159 \, 267 \times 10^{-13} \, \mathrm m\)

by calculation

\(\ds \)

\(\approx\)

\(\ds 3 \cdotp 86159 \, 267 \times 10^{-11} \, \mathrm {cm}\)

by calculation

$\blacksquare$

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $2$. Physical Constants and Conversion Factors: Table $2.3$ Adjusted Values of Constants

which gives the mantissa as $3 \cdotp 861 \, 692$ with an uncertainty of $\pm 12$ corresponding to the $2$ least significant figures